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Scale Factor Practice Problems
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Scale Factor Practice Problems
Work out each answer. Keep units the same when comparing lengths, and show your working where you can.
Finding scale factors
1.A rectangle is 5 cm long. A similar rectangle is 20 cm long. What is the scale factor from the smaller rectangle to the larger one?
2.A triangle has side lengths of 4 cm, 7 cm and 9 cm. Its similar enlarged copy has side lengths of 8 cm, 14 cm and 18 cm. What is the scale factor?
3.Which scale factor makes a shape smaller?
- 1.8
- 1
- 0.6
- 3
4.A side measuring 3 cm on a shape corresponds to a side measuring 15 cm on a similar shape. Complete the statement: the scale factor from the first shape to the second is .
Using scale factors
5.A small photograph is 8 cm wide. It is enlarged by a scale factor of 1.5. What is the width of the enlarged photograph?
6.On a map, 1 cm represents 2 km. Two villages are 7 cm apart on the map. How far apart are they in real life?
7.A garden plan uses the scale 1 cm to 25 cm. A path measures 6 cm on the plan. What is the path's actual length in centimetres?
8.A model tower is made at a scale of 1:20. The real tower is 18 metres tall. How tall is the model in centimetres?
Matching and problem solving
9.Match each original length to the corresponding length after it is enlarged by a scale factor of 3.
- 2 cm
- 5 cm
- 8 cm
- 1.5 cm
- 15 cm
- 4.5 cm
- 24 cm
- 6 cm
10.A rectangle is 6 cm long and 4 cm wide. A similar rectangle is enlarged by a scale factor of 2.5. What are the enlarged rectangle's length and width?
11.A side of a shape is 16 cm long. The corresponding side on a reduced copy is 4 cm long. What is the scale factor from the original shape to the reduced copy?
12.A blueprint shows a room as 9 cm long. The scale is 1 cm to 3 m. What is the room's actual length?
13.A shape has a side of 7 cm. It is enlarged by a scale factor of 4. What is the length of the corresponding side in the enlarged shape?
14.A similar pair of shapes has corresponding sides of 10 cm and 15 cm. What is the scale factor from the smaller shape to the larger shape?
3 printable pages
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